We shall now review some salient points of the construction of the \(B_3-L_2\) 
model. For definiteness, we use the simple bottom-up
construction of
ref. [1]}.
The \( B_3 - L_2 \)  model is constructed by extending the SM gauge group, \(SU(3) \times SU(2)_L \times U(1)_Y\) , by an abelian factor \( U(1)_{B_3-L_2}\)  in a
direct product. This new symmetry is gauged, so it comes with an
electrically neutral force carrier, the \( Z^\prime \)  boson. We also introduce the
flavon field \( \mathopen {}\mathclose {\left( \theta \right)} \) , a SM-singlet complex scalar, which
carries charge \( q_{\theta } \)  under \( U(1)_{B_3-L_2}\) . Table REF  displays
the charges of the fields in the model under the new abelian symmetry. Three
right-handed neutrinos \(\nu _{R_{1,2,3}}\)  are added in order to facilitate
neutrino masses and
mixing. With these fields and charges, \( U(1)_{B_3-L_2}\)  acts vectorially on the
fermions (i.e. acts in the same way on left-handed chiral fermions
as it does on their right-handed partners), and gauge anomaly cancellation
manifestly takes place. There is an implicit assumption in the \(B_3-L_2\)  model
(and other similar models) that
they originate from some more complete ultra-violet model which may be a
semi-simple extension, thus obviating constraints coming from
Landau poles [2]}.
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